Last updated on May 26th, 2025
The cube root of 243 is the value that, when multiplied by itself three times (cubed), gives the original number 243. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, designing structures, density and mass, field of engineering etc.
The cube root of 243 is 6.24025146916. The cube root of 243 is expressed as ∛243 in radical form, where the “ ∛ “ sign is called the “radical” sign. In exponential form, it is written as (243)1/3. If “m” is the cube root of 243, then, m3=243. Let us find the value of “m”.
The cube root of 243 is expressed as 3∛9 as its simplest radical form, since
243 = 3×3×3×3×3
∛243 = ∛(3×3×3×3×3)
Group together three same factors at a time and put the remaining factor under ∛ .
∛243= 3∛9
We can find cube root of 243 through a method, named as, Halley’s Method. Let us see how it finds the result.
Now, what is Halley’s Method?
It is an iterative method for finding cube roots of a given number N, such that, x3=N, where this method approximates the value of “x”.
Formula is ∛a≅ x((x3+2a) / (2x3+a)), where
a=given number whose cube root you are going to find
x=integer guess for the cubic root
Let us apply Halley’s method on the given number 243.
Step 1: Let a=243. Let us take x as 6, since, 63=216 is the nearest perfect cube which is less than 243.
Step 2: Apply the formula. ∛243≅ 6((63+2×243) / (2(6)3+243))= 6.24
Hence, 6.24 is the approximate cubic root of 243.
some common mistakes and solutions are given below:
Find (∛240/ ∛243) × (∛241/ ∛243) × (∛242/ ∛243)
(∛240/ ∛243) × (∛241/ ∛243) × (∛242/ ∛243)
= (∛240× ∛241× ∛242) / (∛243× ∛243× ∛243)
=(∛240× ∛241× ∛242)/ ((243)⅓)3
=(∛240× ∛241× ∛242)/243
=(6.214 × 6.223 × 6.231)/ 243
Answer: (6.214 × 6.223 × 6.231)/ 243
We used the fact that ((243)⅓)3=243 and then found the cube roots of 240,241, and 242 and simplified.
The length, breadth, and height of a cuboid is 5 unit, 4 unit, and 4.5 cm respectively. To find its volume, also find the measure of a side of a cube, whose volume is 243 cubic units.
Volume of a cuboid = length × breadth × height = 5 × 4 × 4.5 cubic units = 90 cubic units.
Given, Volume of a cube = 243 cubic units
⇒ side × side × side = 243 cubic units
⇒ side = ∛243
⇒ side = 6.24 units
Answer: Volume of the cuboid = 90 cubic units
Side length of the cube = 6.24 units
Applied the formula and concept of the volume of a cuboid and cube and solved.
Multiply ∛243 × ∛216
∛243×∛216
= 6.24×6
= 37.44
Answer: 37.44
We know that the cubic root of 216 is 6, hence multiplying ∛216 with ∛243.
What is ∛(243⁶^1/6) ?
∛(2436×1/6)
= (243)1/3
= 6.24…
Answer: 6.24
We solved and simplified the exponent part first using the fact that, (2436×1/6)=243, then solved.
Find ∛(243-(-100)).
∛(243-(-100))
= ∛(243+100)
=∛343
=7
Answer: 7
Simplified the expression, and found out the cubic root of the result.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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